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# On the connection formulas of the third Painlevé transcendent

• We consider the connection problem for the sine-Gordon PIII equation$u_{x x}+\frac{1}{x}u_{x}+\sin u=0,$ which is the most commonly studied case among all general thirdPainlevé transcendents. The connectionformulas are derived by the method of "uniform asymptotics"proposed by Bassom, Clarkson, Law and McLeod (Arch. Rat. Mech.Anal., 1998).
Mathematics Subject Classification: Primary: 33E17, 34M55; Secondary: 35Q53.

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